Kerr稳定性在完全次极端范围
Kerr stability in the full subextremal range
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中文总结 AI 辅助
本文通过推广能量-Morawetz估计至完全次极端范围|a|<m，完成了Kerr稳定性猜想的证明。
中文摘要 AI 辅助
本文中，我们将Sergiu Klainerman与作者的一系列工作\\(\cite{KS-GCM1}\\)、\\(\cite{KS-GCM2}\\)、\\(\cite{KS:Kerr}\\)，Elena Giorgi、Sergiu Klainerman与作者的\\(\cite{GKS22}\\)，以及Dawei Shen的\\(\cite{Shen}\\)中的结果从慢旋转情形\\(|a|\ll m\\)推广到完全次极端范围\\(|a|<m\\)，从而完成了Kerr稳定性猜想的证明。限制\\(|a|\ll m\\)实际上仅通过\\(\cite{GKS22}\\)中建立的波动方程和Bianchi系统的估计引入。为去除这一限制，我们关键依赖于Siyuan Ma与作者的两篇配套论文\\(\cite{MaSz24}\\)和\\(\cite{MaSz26}\\)，其中我们分别证明了在\\(|a|<m\\)的Kerr扰动上非齐次标量波动方程和非齐次Teukolsky方程的能量-Morawetz估计。此外，本文的某些结果在我们的配套论文\\(\cite{Sze}\\)中也有证明。
英文摘要
In the present paper, we extend the results in the sequence of works \cite{KS-GCM1} \cite{KS-GCM2} \cite{KS:Kerr} by Sergiu Klainerman and the author, \cite{GKS22} by Elena Giorgi, Sergiu Klainerman and the author, and \cite{Shen} by Dawei Shen from the slowly rotating regime $|a|\ll m$ to the full subextremal range $|a|<m$, thereby completing the proof of the Kerr stability conjecture. The restriction $|a|\ll m$ enters in fact only through the estimates for wave equations and for the Bianchi system established in \cite{GKS22}. To remove this restriction, we crucially rely on the two companion papers \cite{MaSz24} \cite{MaSz26} by Siyuan Ma and the author, in which we prove energy-Morawetz estimates respectively for the inhomogeneous scalar wave equation and for inhomogeneous Teukolsky equations on perturbations of Kerr with $|a|<m$. Additionally, some of the results of the present paper are proved in our companion paper \cite{Sze}.
